The list decoding framework produces a cover \(\mathcal {L}^{\prime }\)  of the list \(\mathcal {L}(\tilde{y}, \mathcal {C}, \mathcal {C}^{\prime })\) , and, as its final step, corrects the cover to obtain the actual list \(\mathcal {L}(\tilde{y}, \mathcal {C}, \mathcal {C}^{\prime })\)  by running the unique decoding algorithm of \(\mathcal {C}\)  on each entry of \(\mathcal {L}^{\prime }\)  (see [1]} for details).
Using theo:listdecframework with a \((1-2\zeta , \eta )\) -parity sampler and omitting this final step of the algorithm, we can obtain the \(\zeta \) -cover \(\mathcal {L}^{\prime }\)  in time \(n^{O(L+k)} {\mathrm {polylog}}(1/\eta )\) .
